Penelope had four boxes, N, P, Q and R which contained a total of 280 mangoes. She transferred 29 mangoes from Box N to Box P, 72 mangoes from Box P to Box Q and 158 mangoes from Box Q to Box R. The ratio of the number of mangoes in Box N to Box P to Box Q changed from  3 : 5 : 10 to 1 : 3 : 6. How many mangoes were in Box R at first?

	Make p the same (1)x3 = (3)	N (1)	P (2)	Q	R
Before	9 u	3 u	5 u	10 u	?
Change 1	- 87	- 29	+ 29
Change 2			- 72	+ 72
Change 3				- 158	+ 158
After	3 p	1 p	3 p	6 p	?

3 u - 29 = 1 p --- (1)

5 u + 29 - 72 = 3 p
5 u - 43 = 3 p --- (2)

(1) _{x 3}
9 u - 87 = 3 p --- (3)

Make p the same.

(3) = (2)
9 u - 87 = 5 u - 43
9 u - 5 u = 87 - 43
4 u = 44

1 u = 44 ÷ 4 = 11

Total number of mangoes in Box N, Box P and Box Q
= 3 u + 5 u + 10 u
= 18 u

Total number of mangoes in Box R at first
= 280 - 18 u
= 280 - 18 x 11
= 280 - 198
= 82

Answer(s): 82